We characterize a Brownian motion indexed by a semilattice of sets, using the theory of set-indexed martingales: a square integrable continuous set-indexed strong martingale is a Brownian motion if and only if its compensator is deterministic and continuous.
|Number of pages||11|
|Journal||Journal of Theoretical Probability|
|State||Published - Oct 1996|
- Set-indexed Brownian motion
- Strong martingale